Degree Theory on Oriented Infinite Dimensional Varieties and the Morse Number of Minimal Surfaces Spanning a Curve in R n . Part I: n ≥4

1985 ◽  
Vol 290 (1) ◽  
pp. 385 ◽  
Author(s):  
A. J. Tromba
Keyword(s):  
Minimal Surfaces ◽  
Degree Theory ◽  
Infinite Dimensional ◽  
Morse Number

Eigenvalue results for pseudomonotone perturbations of maximal monotone operators

2013 ◽  
Vol 11 (5) ◽  
Author(s):  
In-Sook Kim ◽  
Jung-Hyun Bae
Keyword(s):  
Reflexive Banach Space ◽  
Degree Theory ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Dense Subspace ◽  
Uniformly Convex ◽  
Infinite Dimensional ◽  
Surjectivity Result ◽  
Densely Defined

AbstractLet X be an infinite-dimensional real reflexive Banach space such that X and its dual X* are locally uniformly convex. Suppose that T: X⊃D(T) → 2X* is a maximal monotone multi-valued operator and C: X⊃D(C) → X* is a generalized pseudomonotone quasibounded operator with L ⊂ D(C), where L is a dense subspace of X. Applying a recent degree theory of Kartsatos and Skrypnik, we establish the existence of an eigensolution to the nonlinear inclusion 0 ∈ T x + λ C x, with a regularization method by means of the duality operator. Moreover, possible branches of eigensolutions to the above inclusion are discussed. Furthermore, we give a surjectivity result about the operator λT + C when λ is not an eigenvalue for the pair (T, C), T being single-valued and densely defined.

scholarly journals Lévy’s functional analysis in terms of an infinite dimensional Brownian motion III

1983 ◽  
Vol 90 ◽  
pp. 155-173 ◽  
Author(s):  
Yoshihei Hasegawa
Keyword(s):  
Functional Analysis ◽  
Brownian Motion ◽  
Minimal Surfaces ◽  
Quadratic Forms ◽  
Harmonic Functions ◽  
Dimensional Space ◽  
Probabilistic Methods ◽  
Infinite Dimensional Space ◽  
Infinite Dimensional

The purpose of this paper is to define minimality of surfaces in an infinite dimensional space E by probabilistic methods with the description of the relation between minimal surfaces and harmonic functions on the space E, and to analyze purely analytic properties of a certain class of quadratic forms on the space E.

scholarly journals A new topological degree theory for densely defined quasibounded(S˜+)-perturbations of multivalued maximal monotone operators in reflexive Banach spaces

2005 ◽  
Vol 2005 (2) ◽  
pp. 121-158 ◽  
Author(s):  
Athanassios G. Kartsatos ◽  
Igor V. Skrypnik
Keyword(s):  
Topological Degree ◽  
Degree Theory ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Dense Subspace ◽  
Topological Degree Theory ◽  
Nonlinear Functional ◽  
Infinite Dimensional ◽  
Densely Defined

LetXbe an infinite-dimensional real reflexive Banach space with dual spaceX∗andG⊂Xopen and bounded. Assume thatXandX∗are locally uniformly convex. LetT:X⊃D(T)→2X∗be maximal monotone andC:X⊃D(C)→X∗quasibounded and of type(S˜+). Assume thatL⊂D(C), whereLis a dense subspace ofX, and0∈T(0). A new topological degree theory is introduced for the sumT+C. Browder's degree theory has thus been extended to densely defined perturbations of maximal monotone operators while results of Browder and Hess have been extended to various classes of single-valued densely defined generalized pseudomonotone perturbationsC. Although the main results are of theoretical nature, possible applications of the new degree theory are given for several other theoretical problems in nonlinear functional analysis.

A degree theory for semicondensing vectorfields in infinite dimensional Banach spaces and applications

1980 ◽  
Vol 4 (2) ◽  
pp. 393-405 ◽  
Author(s):  
Rainald Schöneberg
Keyword(s):  
Banach Spaces ◽  
Degree Theory ◽  
Infinite Dimensional

Infinite-dimensional degree theory and stochastic analysis

2010 ◽  
Vol 7 (1) ◽  
pp. 33-65
Author(s):  
A. Al-Hussein ◽  
K. D. Elworthy
Keyword(s):  
Stochastic Analysis ◽  
Degree Theory ◽  
Infinite Dimensional

Transfer operator for infinite dimensional dynamical systems

1998 ◽  
Vol 08 (PR6) ◽  
pp. Pr6-227-Pr6-231
Author(s):  
M. Degli Esposti ◽  
S. Isola
Keyword(s):  
Dynamical Systems ◽  
Transfer Operator ◽  
Infinite Dimensional ◽  
Infinite Dimensional Dynamical Systems
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